This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. Primary support for the subproject and the subproject's principal investigator may have been provided by other sources, including other NIH sources. The Total Cost listed for the subproject likely represents the estimated amount of Center infrastructure utilized by the subproject, not direct funding provided by the NCRR grant to the subproject or subproject staff. The heart is a complex nonlinear system, whose function involves the interaction between mechanical contractions and waves of electrochemical excitation. Heartbeats are the result of the nonlinear behaviors of these electrical and mechanical functions. During normal heartbeats, the waves of excitation generate a coordinated contraction of the muscle, known as normal sinus rhythm. In some situations, the orderly waves develop into a complex dynamical state known as fibrillation, which leads to disorganized muscle contractions. Fibrillation in the atria, although not lethal, leaves a patient feeling tired and may increase the risk of stroke. On the other hand, ventricular fibrillation is more dreadful. During ventricular fibrillation, disorganized contractions of the ventricles fail to eject blood effectively, leading to death within a few minutes if left untreated. Ventricular fibrillation is the main cause of sudden cardiac death, which claims 300,000-400,000 lives a year in the United States. A complete understanding of heart rhythm disorders requires a system-levels investigation on the interaction between electrical, chemical, and mechanical activities on biological scales ranging from ion channels to single cells to multi-cellular tissue and organ. While it is difficult if not impossible to monitor and control all these factors in the lab, mathematical modeling provides a useful tool for this purpose. A systems-level understanding of cardiac nonlinear dynamics will not only improve the ability to predict and prevent lethal heart rhythms but also drives the advance of techniques of mathematical modeling in areas such as model reduction, emergent properties, and multiscale modeling.